Question 1129197

{{{matrix(3,3,a,b,c,d,e,f,g,h,i)}}}


The determinant is:

{{{D = a(ei - fh) -b(di - fg) + c(dh -eg)}}}

{{{matrix(3,3,2, 1, 0,
0, -2, 4,
0 ,1, -3)}}}

{{{D = 2(-2*(-3) - 4*1) - 1(0*(-3) -4*0) + 0(0*1 - (-2)*0)}}}
{{{D = 2(6 - 4) - 1(0*0) + 0(0)}}}
{{{D = 2(2)}}}
{{{D = 4}}}


the matrix 
{{{matrix(3,3,2, 1, 0,
0, -2, 4,
0 ,1, -3)}}}  have inverse because D = 4

If the determinant of the matrix is zero, then it will not have an inverse; the matrix is then said to be singular. Only non-singular matrices have inverses.